/******************************************************************************
 *  Compilation:  javac BST.java
 *  Execution:    java BST
 *  Dependencies: StdIn.java StdOut.java Queue.java
 *  Data files:   https://algs4.cs.princeton.edu/32bst/tinyST.txt  
 *
 *  A symbol table implemented with a binary search tree.
 * 
 *  % more tinyST.txt
 *  S E A R C H E X A M P L E
 *  
 *  % java BST < tinyST.txt
 *  A 8
 *  C 4
 *  E 12
 *  H 5
 *  L 11
 *  M 9
 *  P 10
 *  R 3
 *  S 0
 *  X 7
 *
 ******************************************************************************/

package red.book._3._2;

import java.util.NoSuchElementException;

import edu.princeton.cs.algs4.BinarySearchST;
import edu.princeton.cs.algs4.LinearProbingHashST;
import edu.princeton.cs.algs4.Queue;
import edu.princeton.cs.algs4.RedBlackBST;
import edu.princeton.cs.algs4.ST;
import edu.princeton.cs.algs4.SeparateChainingHashST;
import edu.princeton.cs.algs4.SequentialSearchST;
import edu.princeton.cs.algs4.StdIn;
import edu.princeton.cs.algs4.StdOut;

/**
 *  The {@code BST} class represents an ordered symbol table of generic
 *  key-value pairs.
 *  It supports the usual <em>put</em>, <em>get</em>, <em>contains</em>,
 *  <em>delete</em>, <em>size</em>, and <em>is-empty</em> methods.
 *  It also provides ordered methods for finding the <em>minimum</em>,
 *  <em>maximum</em>, <em>floor</em>, <em>select</em>, <em>ceiling</em>.
 *  It also provides a <em>keys</em> method for iterating over all of the keys.
 *  A symbol table implements the <em>associative array</em> abstraction:
 *  when associating a value with a key that is already in the symbol table,
 *  the convention is to replace the old value with the new value.
 *  Unlike {@link java.util.Map}, this class uses the convention that
 *  values cannot be {@code null}—setting the
 *  value associated with a key to {@code null} is equivalent to deleting the key
 *  from the symbol table.
 *  <p>
 *  This implementation uses an (unbalanced) binary search tree. It requires that
 *  the key type implements the {@code Comparable} interface and calls the
 *  {@code compareTo()} and method to compare two keys. It does not call either
 *  {@code equals()} or {@code hashCode()}.
 *  The <em>put</em>, <em>contains</em>, <em>remove</em>, <em>minimum</em>,
 *  <em>maximum</em>, <em>ceiling</em>, <em>floor</em>, <em>select</em>, and
 *  <em>rank</em>  operations each take
 *  linear time in the worst case, if the tree becomes unbalanced.
 *  The <em>size</em>, and <em>is-empty</em> operations take constant time.
 *  Construction takes constant time.
 *  <p>
 *  For additional documentation, see <a href="https://algs4.cs.princeton.edu/32bst">Section 3.2</a> of
 *  <i>Algorithms, 4th Edition</i> by Robert Sedgewick and Kevin Wayne.
 *  For other implementations, see {@link ST}, {@link BinarySearchST},
 *  {@link SequentialSearchST}, {@link RedBlackBST},
 *  {@link SeparateChainingHashST}, and {@link LinearProbingHashST},
 *
 *  @author Robert Sedgewick
 *  @author Kevin Wayne
 */
public class BST2<Key extends Comparable<Key>, Value> {
    private Node root;             // root of BST

    private class Node {
    	private Key key;
        private Value val;
        private Node left, right;
        private int size;
        
		public Node(Key key, Value val, int size) {
			super();
			this.key = key;
			this.val = val;
			this.size = size;
		}
    }

    /**
     * Initializes an empty symbol table.
     */
    public BST2() {
    }

    /**
     * Returns true if this symbol table is empty.
     * @return {@code true} if this symbol table is empty; {@code false} otherwise
     */
    public boolean isEmpty() {
        return size() == 0;
    }

    /**
     * Returns the number of key-value pairs in this symbol table.
     * @return the number of key-value pairs in this symbol table
     */
    public int size() {
        return size(root);
    }

    // return number of key-value pairs in BST rooted at x
    private int size(Node x) {
    	if(x == null) 
    		return 0;
    	else
    		return x.size;
    }

    public Value get(Key key) {
        return get(root, key);
    }

    private Value get(Node x, Key key) {
    	if(key == null) {
    		throw new IllegalArgumentException("calls get() with a null key");
    	}
    	if(x == null)
    		return null;
    	int cmp = key.compareTo(x.key);
    	if(cmp < 0) {
    		return get(x.left, key);
    	}else if(cmp > 0) {
    		return get(x.right, key);
    	}else {
    		return x.val;
    	}
    }
    
    public void put(Key key, Value val) {
        if (key == null) throw new IllegalArgumentException("calls put() with a null key");
        if (val == null) {
            delete(key);
            return;
        }
        root = put(root, key, val);
        assert check();
    }

    private Node put(Node x, Key key, Value val) {
    	if(x == null) {
    		return new Node(key, val, 1);
    	}
    	int cmp = key.compareTo(x.key);
    	if(cmp < 0) {
    		x.left = put(x.left, key, val);
    	}else if (cmp > 0) {
    		x.right = put(x.right, key, val);
    	}else {
    		x.val = val;
    	}
    	x.size = size(x.left) + size(x.right) + 1;
    	return x;
    }


    /**
     * Removes the smallest key and associated value from the symbol table.
     *
     * @throws NoSuchElementException if the symbol table is empty
     */
    public void deleteMin() {
        if (isEmpty()) throw new NoSuchElementException("Symbol table underflow");
        root = deleteMin(root);
        assert check();
    }

    private Node deleteMin(Node x) {
        if(x.left == null)
        	return x.right;
        x.left = deleteMin(x.left);
        x.size = size(x.left) + size(x.right) + 1;
        return x;
    }

    /**
     * Removes the largest key and associated value from the symbol table.
     *
     * @throws NoSuchElementException if the symbol table is empty
     */
    public void deleteMax() {
        if (isEmpty()) throw new NoSuchElementException("Symbol table underflow");
        root = deleteMax(root);
        assert check();
    }

    private Node deleteMax(Node x) {
       if(x.right == null)
    	   return x.left;
       x.right = deleteMax(x.right);
       x.size = size(x.left) + size(x.right) + 1;
       return x;
    }
    

    /**
     * Removes the specified key and its associated value from this symbol table     
     * (if the key is in this symbol table).    
     *
     * @param  key the key
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public void delete(Key key) {
        if (key == null) throw new IllegalArgumentException("calls delete() with a null key");
        root = delete(root, key);
        assert check();
    }

    private Node delete(Node x, Key key) {
       if(x == null) {
    	   return null;
       }
       int cmp = key.compareTo(x.key);
       if(cmp < 0) {
    	   x.left = delete(x.left, key);
       }else if(cmp > 0) {
    	   x.right = delete(x.right, key);
       }else {
    	   if(x.left == null) {
    		   return x.right;
    	   }
    	   if(x.right == null) {
    		   return x.left;
    	   }
    	   Node t = x;
    	   x = min(x.right);
    	   x.right = deleteMin(x.right);
    	   x.left = t.left;
    	   //! retrun x; 
       }
       x.size = size(x.left) + size(x.right) + 1;
       return x;
    } 


    /**
     * Returns the smallest key in the symbol table.
     *
     * @return the smallest key in the symbol table
     * @throws NoSuchElementException if the symbol table is empty
     */
    public Key min() {
        if (isEmpty()) throw new NoSuchElementException("calls min() with empty symbol table");
        return min(root).key;
    } 

    private Node min(Node x) { 
        if(x.left == null)
        	return x;
        else
        	return min(x.left);
    } 

    /**
     * Returns the largest key in the symbol table.
     *
     * @return the largest key in the symbol table
     * @throws NoSuchElementException if the symbol table is empty
     */
    public Key max() {
        if (isEmpty()) throw new NoSuchElementException("calls max() with empty symbol table");
        return max(root).key;
    } 

    private Node max(Node x) {
    	if(x.right == null)
        	return x;
        else
        	return max(x.right);
    } 

    /**
     * Returns the largest key in the symbol table less than or equal to {@code key}.
     *
     * @param  key the key
     * @return the largest key in the symbol table less than or equal to {@code key}
     * @throws NoSuchElementException if there is no such key
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public Key floor(Key key) {
        if (key == null) throw new IllegalArgumentException("argument to floor() is null");
        if (isEmpty()) throw new NoSuchElementException("calls floor() with empty symbol table");
        Node x = floor(root, key);
        if (x == null) return null;
        else return x.key;
    } 

    private Node floor(Node x, Key key) {
    	if(x == null) {
    		return null;
    	}
        int cmp = key.compareTo(x.key);
        if(cmp < 0)
        	return floor(x.left, key);
        else if(cmp > 0) {
        	Node t = floor(x.right, key);
        	if(t == null)
        		return x;
        	else
        		return t;
        }else
        	return x;
    } 


    /**
     * Returns the smallest key in the symbol table greater than or equal to {@code key}.
     *
     * @param  key the key
     * @return the smallest key in the symbol table greater than or equal to {@code key}
     * @throws NoSuchElementException if there is no such key
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public Key ceiling(Key key) {
        if (key == null) throw new IllegalArgumentException("argument to ceiling() is null");
        if (isEmpty()) throw new NoSuchElementException("calls ceiling() with empty symbol table");
        Node x = ceiling(root, key);
        if (x == null) return null;
        else return x.key;
    }

    private Node ceiling(Node x, Key key) {
    	int cmp = key.compareTo(x.key);
    	if(cmp == 0) {
    		return x;
    	}
    	if(cmp < 0) {
    		Node t = ceiling(x.left, key);
    		if(t == null)
    			return x;
    		else
    			return t;
    	}
    	return ceiling(x.right, key);
    } 

    /**
     * Return the key in the symbol table whose rank is {@code k}.
     * This is the (k+1)st smallest key in the symbol table.
     *
     * @param  k the order statistic
     * @return the key in the symbol table of rank {@code k}
     * @throws IllegalArgumentException unless {@code k} is between 0 and
     *        <em>n</em>–1
     */
    public Key select(int k) {
        if (k < 0 || k >= size()) {
            throw new IllegalArgumentException("argument to select() is invalid: " + k);
        }
        Node x = select(root, k);
        return x.key;
    }
    
    public boolean contains(Key key) {
        if (key == null) throw new IllegalArgumentException("argument to contains() is null");
        return get(key) != null;
    }

    // Return key of rank k. 
    private Node select(Node x, int k) {
    	if(x == null) {
    		return null;
    	}
        int size = size(x.left);
        if(size < k)
        	return select(x.right, k - size - 1);
        else if(size > k)
        	return select(x.left, k);
        else
        	return x;
    } 

    /**
     * Return the number of keys in the symbol table strictly less than {@code key}.
     *
     * @param  key the key
     * @return the number of keys in the symbol table strictly less than {@code key}
     * @throws IllegalArgumentException if {@code key} is {@code null}
     */
    public int rank(Key key) {
        if (key == null) throw new IllegalArgumentException("argument to rank() is null");
        return rank(key, root);
    } 

    // Number of keys in the subtree less than key.
    private int rank(Key key, Node x) {
       if(x == null) {
    	   return 0;
       }
       int cmp = key.compareTo(x.key);
       if(cmp < 0) {
    	   return rank(key, x.left);
       }else if(cmp > 0) {
    	   return size(x.left) + 1 + rank(key, x.right);
       }else {
    	   return size(x.left);
       }
    } 

    /**
     * Returns all keys in the symbol table as an {@code Iterable}.
     * To iterate over all of the keys in the symbol table named {@code st},
     * use the foreach notation: {@code for (Key key : st.keys())}.
     *
     * @return all keys in the symbol table
     */
    public Iterable<Key> keys() {
        if (isEmpty()) return new Queue<Key>();
        return keys(min(), max());
    }

    /**
     * Returns all keys in the symbol table in the given range,
     * as an {@code Iterable}.
     *
     * @param  lo minimum endpoint
     * @param  hi maximum endpoint
     * @return all keys in the symbol table between {@code lo} 
     *         (inclusive) and {@code hi} (inclusive)
     * @throws IllegalArgumentException if either {@code lo} or {@code hi}
     *         is {@code null}
     */
    public Iterable<Key> keys(Key lo, Key hi) {
        if (lo == null) throw new IllegalArgumentException("first argument to keys() is null");
        if (hi == null) throw new IllegalArgumentException("second argument to keys() is null");

        Queue<Key> queue = new Queue<Key>();
        keys(root, queue, lo, hi);
        return queue;
    } 

    private void keys(Node x, Queue<Key> queue, Key lo, Key hi) { 
        
    } 

    /**
     * Returns the number of keys in the symbol table in the given range.
     *
     * @param  lo minimum endpoint
     * @param  hi maximum endpoint
     * @return the number of keys in the symbol table between {@code lo} 
     *         (inclusive) and {@code hi} (inclusive)
     * @throws IllegalArgumentException if either {@code lo} or {@code hi}
     *         is {@code null}
     */
    public int size(Key lo, Key hi) {
        if (lo == null) throw new IllegalArgumentException("first argument to size() is null");
        if (hi == null) throw new IllegalArgumentException("second argument to size() is null");

        if (lo.compareTo(hi) > 0) return 0;
        if (contains(hi)) return rank(hi) - rank(lo) + 1;
        else              return rank(hi) - rank(lo);
    }

  /*************************************************************************
    *  Check integrity of BST data structure.
    ***************************************************************************/
    private boolean check() {
        if (!isBST())            StdOut.println("Not in symmetric order");
        if (!isSizeConsistent()) StdOut.println("Subtree counts not consistent");
        if (!isRankConsistent()) StdOut.println("Ranks not consistent");
        return isBST() && isSizeConsistent() && isRankConsistent();
    }

    // does this binary tree satisfy symmetric order?
    // Note: this test also ensures that data structure is a binary tree since order is strict
    private boolean isBST() {
        return isBST(root, null, null);
    }

    // is the tree rooted at x a BST with all keys strictly between min and max
    // (if min or max is null, treat as empty constraint)
    // Credit: Bob Dondero's elegant solution
    private boolean isBST(Node x, Key min, Key max) {
        if (x == null) return true;
        if (min != null && x.key.compareTo(min) <= 0) return false;
        if (max != null && x.key.compareTo(max) >= 0) return false;
        return isBST(x.left, min, x.key) && isBST(x.right, x.key, max);
    } 

    // are the size fields correct?
    private boolean isSizeConsistent() { return isSizeConsistent(root); }
    private boolean isSizeConsistent(Node x) {
        if (x == null) return true;
        if (x.size != size(x.left) + size(x.right) + 1) return false;
        return isSizeConsistent(x.left) && isSizeConsistent(x.right);
    } 

    // check that ranks are consistent
    private boolean isRankConsistent() {
        for (int i = 0; i < size(); i++)
            if (i != rank(select(i))) return false;
        for (Key key : keys())
            if (key.compareTo(select(rank(key))) != 0) return false;
        return true;
    }


    /**
     * Unit tests the {@code BST} data type.
     *
     * @param args the command-line arguments
     */
    public static void main(String[] args) { 
    	BST<String, Integer> st = new BST<String, Integer>();
        st.put("S", 1);
        st.put("E", 1);
        st.put("A", 1);
        st.put("C", 1);
        st.put("H", 1);
        st.put("R", 1);
        st.put("X", 1);
        st.put("M", 1);
        
        for (String s : st.keys())
            StdOut.println(s + " " + st.get(s));
        System.out.println(st.max());
        System.out.println(st.floor("G"));
        System.out.println(st.ceiling("U"));
    }
    
	public void print(Node x){
    	if (x == null) return;
    	print(x.left);
    	StdOut.println(x.key);
    	print(x.right);
   }
}